In analyzing and developing oilfields, it is common to drill wellbores in the formation containing a hydrocarbon reservoir for the purpose of running tools down the wellbore(s) in order to generate data useful in analyzing the makeup of the formation and the contents of the reservoir. Some of the commonly run tools include resistivity tools, spectroscopy tools, and dielectric scanning tools. Nuclear magnetic resonance (NMR) tools and acoustic tools are also often run. The data obtained from the tools are regularly used to analyze and model the geological formation and the reservoir. Information regarding the rock matrix and the fluid volume, such as porosity, permeability, hydrocarbon volume, water and oil saturations, conductivities, etc., are desired results.
Interpretation models are used to estimate water saturation Sw, water salinity, and an effective cementation exponent mn from measured dielectric data. The parameter mn is known to combine multiple effects including the effect of pore space tortuosity, which is captured by a cementation exponent m, and the distribution of water and hydrocarbons in the pore system, which is captured by a saturation exponent n in the well-known Archie's equation.
Parameter mn has several applications. When the value of m can be estimated through measurements such as measurements from a nuclear magnetic resonance (NMR) tool or from a full bore micro resistivity imager tool, such as FMI-HD™ (a trademark of Schlumberger Technology Corporation), or from core resistivity measurements, the parameter mn may be used to estimate n which can then be used to infer information about wettability. In addition, mn obtained in a shallow (e.g., invaded) zone by downhole dielectric tools is used to estimate water saturation in the deep (e.g., virgin) zone using deep resistivity tools and Archie's law. These applications, however, are limited in scope for several reasons. First, NMR, micro resistivity imager, or core measurements may not be available to provide a value for parameter m. Second, due to mud invasion in the formation, water saturation values in the shallow and deep zones are likely to be different. Since mn is saturation dependent, an invaded zone mn can be used to derive water saturation in the virgin zone only if their saturations are the same or when m=n.